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+ 
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012  Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ORDERING_H
+#define EIGEN_ORDERING_H
+
+#include <Eigen_Colamd.h> 
+#include <Amd.h>
+
+namespace Eigen {
+template<class Derived> 
+class OrderingBase
+{
+  public:
+    typedef typename internal::traits<Derived>::MatrixType MatrixType;
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename MatrixType::Index Index;
+    typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType;
+  
+  public:
+    OrderingBase():m_isInitialized(false)
+    {
+      
+    }
+    OrderingBase(const MatrixType& mat):OrderingBase()
+    {
+      compute(mat);
+    }
+    Derived& compute(const MatrixType& mat)
+    {
+      return derived().compute(mat);
+    }
+    Derived& derived()
+    {
+      return *static_cast<Derived*>(this);
+    }
+    const Derived& derived() const
+    {
+      return *static_cast<const Derived*>(this);
+    }
+    /** 
+     * Get the permutation vector 
+     */
+    PermutationType& get_perm(const MatrixType& mat)
+    {
+      if (m_isInitialized = true) return m_P; 
+      else abort(); // FIXME Should find a smoother way to exit with error code
+    }
+    template<typename MatrixType> 
+    void at_plus_a(const MatrixType& mat);
+    
+    /** keeps off-diagonal entries; drops diagonal entries */
+    struct keep_diag {
+      inline bool operator() (const Index& row, const Index& col, const Scalar&) const
+      {
+        return row!=col;
+      }
+    };
+    
+  protected:
+    void init()
+    {
+      m_isInitialized = false;
+    }
+    PermutationType m_P; // The computed permutation 
+    mutable bool m_isInitialized; 
+    SparseMatrix<Scalar,ColMajor,Index> m_mat; // Stores the (symmetrized) matrix to permute
+}
+/**
+ * Get the symmetric pattern A^T+A from the input matrix A. 
+ * NOTE: The values should not be considered here
+ */
+template<typename MatrixType>
+void OrderingBase::at_plus_a(const MatrixType& mat)
+{
+    MatrixType C;
+    C = mat.transpose(); // NOTE: Could be  costly
+    for (int i = 0; i < C.rows(); i++) 
+    {
+        for (typename MatrixType::InnerIterator it(C, i); it; ++it)
+          it.valueRef() = 0.0;
+    }
+    m_mat = C + mat; 
+
+/** 
+ * Get the column approximate minimum degree ordering 
+ * The matrix should be in column-major format
+ */
+template<typename Scalar, typename Index>
+class COLAMDOrdering: public OrderingBase< ColamdOrdering<Scalar, Index> >
+{
+  public:
+    typedef OrderingBase< ColamdOrdering<Scalar, Index> > Base;
+    typedef SparseMatrix<Scalar,ColMajor,Index> MatrixType;  
+    
+  public:
+    COLAMDOrdering():Base() {}
+    
+    COLAMDOrdering(const MatrixType& matrix):Base()
+    {
+      compute(matrix);
+    }
+    COLAMDOrdering(const MatrixType& mat, PermutationType& perm_c):Base()
+    {
+      compute(matrix); 
+      perm_c = this.get_perm();
+    }
+    void compute(const MatrixType& mat)
+    {
+      // Test if the matrix is column major...
+          
+      int m = mat.rows();
+      int n = mat.cols();
+      int nnz = mat.nonZeros();
+      // Get the recommended value of Alen to be used by colamd
+      int Alen = colamd_recommended(nnz, m, n); 
+      // Set the default parameters
+      double knobs[COLAMD_KNOBS]; 
+      colamd_set_defaults(knobs);
+      
+      int info;
+      VectorXi p(n), A(nnz); 
+      for(int i=0; i < n; i++) p(i) = mat.outerIndexPtr()(i);
+      for(int i=0; i < nnz; i++) A(i) = mat.innerIndexPtr()(i);
+      // Call Colamd routine to compute the ordering 
+      info = colamd(m, n, Alen, A,p , knobs, stats)
+      eigen_assert( (info != FALSE)&& "COLAMD failed " );
+      
+      m_P.resize(n);
+      for (int i = 0; i < n; i++) m_P(p(i)) = i;
+      m_isInitialized = true;
+    }
+  protected:
+    using Base::m_isInitialized;
+    using Base m_P; 
+}
+
+/** 
+ * Get the approximate minimum degree ordering
+ * If the matrix is not structurally symmetric, an ordering of A^T+A is computed
+ * \tparam Scalar The type of the scalar of the matrix for which the ordering is applied
+ * \tparam  Index The type of indices of the matrix 
+ * \tparam _UpLo If the matrix is symmetric, indicates which part to use
+ */
+template <typename Scalar, typename Index, typename _UpLo>
+class AMDordering : public OrderingBase<AMDOrdering<Scalar, Index> >
+{
+  public:
+    enum { UpLo = _UpLo };
+    typedef OrderingBase< AMDOrdering<Scalar, Index> > Base;
+    typedef SparseMatrix<Scalar, ColMajor,Index> MatrixType;  
+  public:
+    AMDOrdering():Base(){}
+    AMDOrdering(const MatrixType& mat):Base()
+    {
+      compute(matrix);
+    }
+    AMDOrdering(const MatrixType& mat, PermutationType& perm_c):Base()
+    {
+      compute(matrix); 
+      perm_c = this.get_perm();
+    }
+    /** Compute the permutation vector from a column-major sparse matrix */
+    void compute(const MatrixType& mat)
+    {
+      // Compute the symmetric pattern
+      at_plus_a(mat); 
+    
+      // Call the AMD routine 
+      m_mat.prune(keep_diag());
+      internal::minimum_degree_ordering(m_mat, m_P);
+      if (m_P.size()>0) m_isInitialized = true;
+    }
+    /** Compute the permutation with a self adjoint matrix */
+    template <typename SrcType, unsigned int SrcUpLo> 
+    void compute(const SparseSelfAdjointView<SrcType, SrcUpLo>& mat)
+    {
+      m_mat = mat;
+      
+      // Call the AMD routine 
+      m_mat.prune(keep_diag());
+      internal::minimum_degree_ordering(m_mat, m_P);
+      if (m_P.size()>0) m_isInitialized = true;
+    }
+  protected:
+    using Base::m_isInitialized;
+    using Base::m_P;
+    using Base::m_mat;
+}
+
+} // end namespace Eigen
+#endif
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